Analysis of Out-of-Plane Measurments of the Fifth Structure Function of the Deuteron

We have measured the $D(\vec e,e^\prime p)n$ reaction and the asymmetry $A_{LT}^\prime$ associated with the fifth structure function in quasi-elastic electron scattering from deuterium at a beam energy of 2.56 GeV and over the range $\rm Q^2 = 0.1-2.0 ~ GeV^2$ with the CLAS detector at Jefferson Lab. The data were collected using both magnet polarities to explore different $\rm Q^2$ regions. We extracted $A_{LT}^\prime$ as a function of missing momentum ($p_m$) using spectra weighted by $\sin \phi_{pq}$ where $\phi_{pq}$ is the angle between the electron scattering plane and the plane defined by the ejected proton and 3-momentum transfer. We compared the measured $A_{LT}^\prime$ with a calculation by Jeschonnek and Van Orden by averaging over the $\rm Q^2$ distribution of the CLAS data. The theoretical curves largely agree with the 2.56-GeV data at $\rm Q^2=0.6-2.0~ GeV^2$, but diverge from the data for low $\rm Q^2$ ($\rm 0.1-1.0~ GeV^2$) and high $p_m$ (greater than 0.4 GeV). To understand the systematic uncertainties on $A_{LT}^\prime$ we varied the positions of the kinematic cuts used to define quasielastic scattering and the final state proton. The results showed systematic uncertainties of about 1\% or less in regions of high statistics.